where \(\langle \cdots \rangle _{\rm CFT}\)  denotes averaging in the free field theory and \(\int V_b(u){\rm d}u\)  is a screening charge, it is nothing but the four-point conformal block [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}. At the same time, the degenerate five-point conformal block \(G_5=\langle V_{1/2b}(z)\cdots \rangle _{\rm CFT}\) . Since \(\langle V_{1/2b}(z)V_b(u)\rangle _{\rm CFT}=z-u\) , one immediately obtains \(G_5=\langle \det (z-u_i)\rangle \) . From (REF ) one knows that the matrix model average of the determinant satisfies the equation for the quantum spectral curve. Hence, the equation (REF ) for \(G_5\)  is exactly the quantum spectral curve for the Dotsenko–Fateev (or conformal) matrix model (REF ).
